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Unformatted text preview: Modern Physics-1 A Brief History of Modern Physics and the development of the Schrödinger Equation "Modern" physics means physics discovered after 1900; i.e. twentieth-century physics. 1900: Max Planck (German) tried to explain blackbody radiation using Maxwell's equations and statistical mechanics and found that he could not. He could only reproduce the experimentally-known BB spectrum by assuming that the energy in an electromagnetic wave of frequency f is quantized according to EM wave E n h f = , where n = 1, 2, 3, … and h = Planck's constant = 6.6 × 10- 34 (SI units) Planck regarding this as a math trick; he was baffled by its physical significance. 1905: Albert Einstein , motivated in part by Planck's work, invents the concept of a photon to explain the photoelectric effect. A photon is a quantum (packet) of electromagnetic radiation, with energy E h f γ = = ϖ h . 1911: Ernest Rutherford (New Zealand/Britain) shows that an atom consists of a small, heavy, positively-charged nucleus, surrounded by small light electrons. But there is a problem with the classical theory of this nuclear atom: An electron in orbit about a nucleus is accelerating and, according to Maxwell's equations, an accelerating charge must radiate (give off EM radiation). As the electron radiates, giving energy, it should spiral into the nucleus. 1913: Niels Bohr (Danish), a theorist working in Rutherford's lab, invents the Bohr model. This is essentially a classical model, treating the electron as a particle with a definite position and momentum, but the model has two non-classical, ad hoc assumptions: 1) The angular momentum of the electron is quantized: L n = h . 2) The electron orbits, determined by (1), are stable ("stationary"), do not radiate, unless there is a transition between two orbits, and then the atom emits or absorbs a single photon of energy f i h f E E =- The predictions of Bohr model match the experimental spectrum of hydrogen perfectly. It is important to remember that the Bohr model is simple, useful, and wrong . For instance, it predicts that the ground state of the H-atom has angular momentum L = h , when in fact, the ground state of the H atom (s-state) has L = 0. The Bohr model is a semi-classical model , meaning it combines aspects of classical and quantum mechanics. Semi-classical models are frequently used by physicists because they are heuristically useful (easy to understand and often give correct results). But they must always be used Last update: 2/27/2012 Dubson Phys3220 Notes, University of Colorado Classically, an electron in an atom should radiate and spiral inward as it loses energy. Modern Physics-2...
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